It is shown that a generally complex-valued function of a real variable is a solution of a classical Sturm- Liouville eigenvalue problem if and only if a related twoparameter eigenvalue problem for a pair of integral operators, one of which is of Hammerstein type, admits a real solution belonging to a cone in a Krein space.

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Keywords Hammerstein, Krein space, Sturm-Liouville
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Journal Journal of Integral Equations and Applications
Mingarelli, A. (1992). Sturm-liouville problems and Hammerstein operators. Journal of Integral Equations and Applications, 4(1), 83–88. doi:10.1216/jiea/1181075667